腔光力学主要是研究腔场和机械振子之间由于存在光压所形成的相互作用，利用腔光力系统可以实现腔场对机械振子的量子控制或者机械振子对腔场的量子调控。由于微加工技术的不断进步，在实验上已经能够生产出纳米量级的机械振子，使得腔光力系统的空间尺度更加小，而其所产生的量子效应也更加突出，促进了量子与经典物理之间界限的揭示。目前多种光力系统被提出，实验和理论方面都取得了一系列重要研究成果，如引力波探测、微小位移和质量的测量、光力诱导透明效应、光子阻塞效应和量子纠缠等，本论文在这些研究成果的基础上，对双拉盖尔-高斯腔光力系统中的探测响应和纠缠现象进行研究。

首先，基于双拉盖尔-高斯旋转振动腔，研究系统内的探测响应现象。通过理论计算得到探测场传输系数的表达式，结果表明系统内会存在三个诱导透明窗口，包括一个耦合共振诱导透明（CRIT）窗口，两个由螺旋相位片的转动和振动自由度分别与腔内场作用产生的光力诱导透明（OMIT）窗口。通过改变两腔间的耦合系数、拉盖尔-高斯驱动光场携带的拓扑电荷数和单光子光力耦合系数可以实现对三个窗口的深度和宽度的单独控制。此外改变振动和旋转模式的频率能够完成一个窗口到三个窗口的转换，当这两个频率相等时，三个窗口合成为一个。最后我们分析系统内存在的慢光效应，这些结果对实验上实现可控的多诱导透明窗口以及研究多路径干涉具有参考意义。

其次，基于双拉盖尔-高斯旋转腔，研究跨腔旋转端镜之间的量子纠缠现象。研究表明，选定相关参数，系统腔内的光子和端镜声子之间存在稳定的量子光力纠缠，纠缠值受腔间耦合系数和拉盖尔-高斯驱动光场携带的拓扑电荷数的影响。与此同时引入两腔之间的耦合，可以使跨越两个腔的旋转端镜之间形成量子纠缠，证明在该系统内能够完成从光子-声子纠缠到声子-声子纠缠的转移，从而实现宏观远距离量子纠缠。我们分析了该纠缠值随拓扑电荷数、腔间耦合系数和腔场耗散的变化关系，在特定的参数下能够产生最大纠缠，即使是在不可分辨边带条件下纠缠仍然存在，且该纠缠对温度有很好的鲁棒性。

The cavity-optomechanical system is mainly used to study the radiation-pressure interaction between optical fields and mechanical resonators, one can not only obtain the methods of quantum control of the mechanical motion but also access the ways of mechanical control of the optical fields in the system. With the development of micromechanical technology, a nano mechanical resonator can be manufactured experimentally to lead some more obvious quantum effects, it can be a boost for revealing the boundary between quantum physics and classical physics. So far a variety of cavity-optomechanical systems have been proposed and many important achievements have been made in the experimental and theoretical fields, such as gravitational-wave detectors, high-precision measurements of mass and displacement, optomechanical induced transparency, photon blockade effect and quantum entanglement. This paper primarily focuses on the probe response and the quantum entanglement between two resonators in a optomechanical system consisting of two Laguerre-Gaussian cavities.

Firstly, we study the probe response in the system consisting of a Laguerre-Gaussian (L-G) rovibrational cavity and a L-G fixed cavity. The transmission coefficient is obtained theoretically, which shows that there are three induced transparency windows, including a coupled-resonator-induced transparency (CRIT) window and two optomechanically induced transparency (OMIT) windows that are induced by the vibration mode and the rotation mode of rovibrational mirror coupled with the radiation field in the cavity. The depth and width of these three windows can be controlled separately by changing the coupling coefficient between two cavities, the number of optical charges carried by the L-G beam and the optomechanical single-photon coupling strength. In addition, the conversion from the one-window mode to the three-window mode can be completed by changing the frequency of the vibration mode and rotation mode of the rovibrational mirror. When their frequency are same, these three windows will combine into one. Finally, we analyze the slow-light effect in the system. These results have important reference value for realizing the controllable multi-induced transparency windows and studying the multipath quantum interference taking place in the system experimentally.

Secondly, we study the quantum entanglement between two rotational mirrors in the system consisting of two L-G rotational cavities. It is shown that there is a stable optomechanical entanglement between the radiation field and the rotational mirror of the system with selected parameters, such as the coupling coefficient between two cavities and the number of optical charges carried by the driving L-G beam. At the same time, the quantum entanglement of the two rotational mirrors can be formed by adding the coupling between the two cavities, which shows the transfer from photon-photon entanglement to phonon-phonon entanglement, and it is particularly important for studying the macroscopic long-range quantum entanglement. We analyze the relationship between phonon-phonon entanglement and the optical charge, the the coupling coefficient of two cavities and the decay rates of the cavity and the mirror, and obtain the entanglement robust to temperature even outside the resolved-sideband regimes.